The decisive role female voters may play in the key battleground state of New Hampshire hasn't been lost on President Obama and his political allies.

If Democrats sweep the swing state's major races on Election Day, New Hampshire would become the first state to have women hold its entire congressional delegation and the governor's office. Obama would also pick up four potentially crucial electoral votes.

"We have held hundreds of events targeting women voters," said Harrell Kirstein, a spokesman for the Obama campaign in New Hampshire.

These have ranged from "Women's Wednesdays" mixers to visits by fair pay advocate Lilly Ledbetter and Democratic National Committee Chairwoman Debbie Wasserman Schultz. On Wednesday, Cecile Richards, president of the Planned Parenthood Action Fund, visited New Hampshire to kick off a multitown phone-banking effort.

Republican Mitt Romney also has made New Hampshire a focus of his campaign, both in ad spending and on-the-ground appearances. He has an event scheduled on Oct. 30 in Manchester, just a week before the election, and his campaign is focusing on a get-out-the-vote effort.

Romney also has used New Hampshire Republican Sen. Kelly Ayotte as a prolific surrogate for Romney in the state. Ayotte, who at one point was discussed as a potential running mate for Romney, helped the GOP do well with women locally in 2010, when she was easily elected to the Senate.

"This is an important state. It's an important state in large part because of the state Legislature," Richards said.

It's no coincidence Richards makes that argument. During a rally in Manchester last week, Obama went so far as to suggest state politics might have a coattail effect — up ticket.

"You've got a state Legislature up here that sometimes acts like it knows better than women when it comes to women's own health care decisions," Obama said. "Well, my opponent's got the same approach."

In 2010, Republicans swept to 3 to 1 majorities in Concord. While members of the GOP stressed fiscal issues on the campaign trail, abortion and women's health care issues became flash points once they took office.

Republicans moved to block a state contract with Planned Parenthood and pushed bills to limit abortion. They also tried to undo a 12-year-old law requiring insurers to include contraception coverage in all prescription drug plans.

All of these controversies tend to get mentioned in the stump speeches of Democratic gubernatorial candidate Maggie Hassan.

"What's important to understand is that we respect women, their ability to make their own decisions, and that's why we stay focused on the fact that this is just not a place where government should interfere," Hassan said.

The GOP nominee for governor, Ovide Lamontagne, supported a Human Life Amendment, which would give constitutional protections to fetuses, when he ran for U.S. Senate two years ago. For him, restricting abortion has been a longtime goal, but it wouldn't, he insists, be a top priority if he wins the corner office.

"I am not running to advance that agenda; I am running on a jobs and economy agenda," he said.

Even so, the most recent University of New Hampshire Survey Center poll showed big gender-gap edges for Democrats. Obama had a 23-point edge over Romney among female voters; Hassan led Lamontagne by 18 points with women.

Lamontagne's newest radio ad suggests he hopes to reduce that gap. It features Ayotte, the most prominent Republican woman in elective office in the state, who opposes legal abortion in most instances. The ad focuses on taxes, but it's called, tellingly perhaps, "One of Us."